aio SOLVTIO PROBLEMATIS GEOMETRICI 



§. 6. Cum ergo debeat erte A firf. 7 : A fin. § — 

 C 2 :? 2 , atque diuerfi arcus circulares algebraice affignari 

 nequeant, nifi rationem teneant rationalem ,, ante omnia 

 requiritur vt ratio C 2 :^ 2 fit rationalis. Sit igitur C 2 : 

 ^ a r=N:« denotantibus N et n numeros integros, eritque 

 wA fin. y-NA fm. §*; atque porro debebit effe finu s 

 arcus^. A fin. ~==:fin. arcus N.A fm. §. Ex inuentione 

 autem finuum arcuum multiplorum conftat efTe finum 



n — 1 n — z 



b nbff — b 2 ) 2 n f n-i^n-i)bHc z -'f) 2 

 arcus «Afm. - = — ^ I# 2m 3 6 * 



•^- 



n (n-i Hn-z)(n-z)(n-4W(c*-b 9 ) 2 



— » etc* 



c 2. 3. 4- 5 ^* 



fimilique modo fmus arcns N.A fin. §- exprimetur* 

 Qmmobrem fequens habebitur aequatio algebraica 



nb(c*-fr)^_ _ n(n- i ){n-i)b'(c 2 -b>) - 



TT~V " 1. a.p 3 ** "T 



5 



— — tt ecc. — . 



1. 2. 3- 4- 5- ' 



NB(C 2 -B 2 r^ N(N-i)(N-sQB* (C*-B 2 )~ ^ 

 -^T"^" ~ 1. ' a. 3. C N ^ 



NfN-OfN-OfN-sUN-^lB^O-B 2 )-^ 



1. 2, 3. 4- 5. <- N 



quae aequatio ob N et n numeros integros femper fini- 

 to conftabit terminorum numero, ex eaque licebit pro 



dat* 



